Former President Donald Trump’s lawyers urged the Supreme Court to weigh in on the FBI’s search of his Mar-a-Lago home, opening the door for the top U.S. court to address the unprecedented investigation.

In a filing Tuesday, Mr. Trump’s legal team said an appeals court had improperly limited a third-party arbiter’s review of the materials the FBI seized during its August search—in which agents removed some 11,000 documents from the Florida resort, including about 100 marked as classified.

The U.S. 11th Circuit Court of Appeals in Atlanta last month sided with the Justice Department and took those classified documents out of the purview of the court-appointed arbiter, or “special master,” allowing prosecutors to resume access to them.

Mr. Trump’s lawyers said the special master should review the documents marked as classified to ensure fairness and instill public confidence in the investigation. They also argued that the 11th Circuit lacked jurisdiction to issue its order.